In known tools of this type (EP 0 428 116, U.S. Pat. No. 4,371,010, U.S. Pat. No. 3,976,108), the clamp parts are pivotably borne by means of an articulation point directly at the tool body, while at another articulation point there engages an actuating element by which the opening and closing movement is generated. In the course of opening, the clamp parts pivot so far to the side in the circular arc that an article to be fastened can be guided through. The wraparound clamp is closed around the article to be fastened and forms, in this condition, a closed guide for a band to be wrapped around the article. In a further known fastening tool (U.S. Pat. No. 3,810,498), the wraparound clamp does not need to be closed completely, specifically in circumstances in which an excessively large article is situated between the clamps and a complete closing of the clamps is not possible; in this case, it is tolerated that in the circumstances no completely closed guide for the band is available. The band is guided in the guide around the article. The lock for fastening the band may be a separate part or may be connected in integral fashion to the rear end of the band. At the very latest, at the end of the wraparound process, it is received by the lock mount. The leading end of the band is then guided through an opening in the lock and grasped by the tensioning device. In the course of tensioning, the band is set onto the article; in this case, the article is drawn to the lock mount or, if the article is stationary, the tool with its lock mount is drawn to the article. This presupposes that sufficient space for the clamp parts projecting from the tool body is present beyond the article. However, in many cases an obstruction is situated in the vicinity, beyond the article; this may be, for example, a carrying structure in the cases in which the band serves to secure the article to a securing lug which, for its part, is connected to the carrying structure. In these circumstances, the clamp parts projecting from the tool body impact against the carrying structure and thus prevent a situation in which the tool can be drawn to the article. Instead, a force is exerted on the article, which force tends to draw it to the lock mount; in this case, a resultant disadvantageous consequence may be that the article is moved out of its position, whereby it itself or components such as the securing lugs which seek to hold it in its position may be damaged. Furthermore, a fastening tool is known (U.S. Pat. No. 3,621,889), in which, during the tensioning procedure, the lock mount is moved away from the tool body, i.e. runs towards the article to be fastened. This does indeed reduce the risk of damage to components which hold the article to be fastened in its position, but, in this case, it is a disadvantage that it may happen that, after the fastening procedure, the band does not have the desired band tension, since it was not possible for the lock mount to approach the article fully. The known tools frequently make additional, costly manual work necessary.